多变量函数空间上具有抽象Volterra算子的不动点方程

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI:10.2298/aadm180615016p

A. Petruşel, I. Rus

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引用次数: 1

摘要

一元函数空间上的抽象Volterra算子的几个概念是众所周知的。本文引入了多变量函数空间中抽象Volterra算子的各种概念。还研究了具有这种抽象Volterra算子的不动点方程。逐步收缩理论的基本要素是g收缩的概念。通过在Darboux-Ionescu问题理论中的应用，说明了逐级收缩原理的相关性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fixed point equations with abstract Volterra operators on spaces of functions of several variables

Several notions of abstract Volterra operators on spaces of functions of one variable are well known. In this paper, we introduce various notions of abstract Volterra operators in spaces of functions of several variables. Some fixed point equations with such abstract Volterra operators are also studied. The basic ingredient in the theory of step by step contraction is the notion of G-contraction. The relevance of step by step contraction principle is illustrated by applications in the theory of Darboux-Ionescu problem.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).